Finite Group Databasebeta

← #15757125

Subgroups — #15757125

Order 3328.

546 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117787C211yesmaximal, characteristic
2#13115592C211yesmaximal, characteristic, complemented
3#13114833C211yesmaximal, characteristic
4C2×#11718051C211yesmaximal, characteristic
5#13112719C211yesmaximal, characteristic, complemented
6#13112676C211yesmaximal, characteristic, complemented
7C13×#1844C211yesmaximal, characteristic, complemented
8C2×#88146—21no—
9C2×C4×D52C2211yescharacteristic
10C2×C13×#106—22no—
11C2×C4×C8×C13C2211yescharacteristic
12C13×#384C2211yescharacteristic
13C13×#384C2211yescharacteristic
14#11718651—22no—
15#11718649—21no—
16#11718648—21no—
17C4⋊C4×Dic13—21no—
18C2×#88049—21no—
19C2×#88047—21no—
20C4×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23#11718121—21no—
24#11718121—21no—
25#11718051C414yescomplemented
26C22×D52D411yescharacteristic
27C22×C4×D13—21no—
28C22×C8×C13—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D412yes—
35C2×C42×C13C2311yescharacteristic
36C2×#6103—21no—
37C2×#6103—22no—
38C2×#6103—22no—
39C2×C4⋊Dic13D411yescharacteristic
40C2×C4⋊Dic13D411yescharacteristic
41C2×C4⋊Dic13D411yescharacteristic
42C2×C4×Dic13—22no—
43C2×C4×Dic13—21no—
44C22×#1055—21no—
45C22×#1055—21no—
46#88146—42no—
47#88146—42no—
48C4×D52—21no—
49C4×D52—21no—
50C4×D52C2×C412yes—
51C4×D52Q812yes—
52C13×#106—44no—
53C4×C8×C13—21no—
54C4×C8×C13C2×C412yes—
55#88071—22no—
56#88071—21no—
57#88049—42no—
58#88047—42no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055C2×C412yes—
63#8889—131nomaximal, Sylow
64C23×D13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—41no—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52C4⋊C412yes—
79C2×C4×D13—22no—
80C2×C4×D13—22no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C8×C13—22no—
86C2×C8×C13—22no—
87C2×C8×C13—22no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C42×C13C22×C411yescharacteristic
99C42×C13C2×Q811yescharacteristic
100C42×C13#4111yescharacteristic
101C42×C13#4111yescharacteristic
102#6103—22no—
103#6103—22no—
104#6103—44no—
105#6103—82no—
106C4⋊Dic13—21no—
107C4⋊Dic13—21no—
108C4⋊Dic13—21no—
109C4⋊Dic13—21no—
110C4⋊Dic13C4⋊C412yes—
111C4⋊Dic13SD1612yes—
112C4×Dic13—44no—
113C4×Dic13—41no—
114C4×Dic13—41no—
115C2×#1055—22no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#1055—41no—
121#2354—131no—
122#1947—131no—
123#1844D1311yescharacteristic, complemented
124#1802—131no—
125C2×D4⋊C8—131no—
126#1296—131no—
127#1279—131no—
128C23×C13#12011yescharacteristic
129C22×D13—22no—
130C22×D13—41no—
131C22×D13—41no—
132C22×D13—41no—
133C22×D13—41no—
134C22×D13—41no—
135C22×D13—41no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13C2×C4⋊C411yescharacteristic
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13C22⋊Q811yescharacteristic
148C2×C4×C13C22⋊Q811yescharacteristic
149C2×C4×C13#12311yescharacteristic
150C2×C4×C13C2×SD1611yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13#13511yescharacteristic
153C2×C4×C13#13511yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C13#13711yescharacteristic
158C2×Dic13—22no—
159C2×Dic13—22no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167D52—22no—
168D52—22no—
169D52—41no—
170D52—41no—
171C4×D13—42no—
172C4×D13—42no—
173C4×D13—42no—
174C4×D13—42no—
175C8×C13—24no—
176#1055—42no—
177#1055—81no—
178C2×C4×D4—131no—
179C2×#117—261no—
180C2×#107—261no—
181C2×#106—22no—
182C2×C4⋊C8—131no—
183C2×C4⋊C8—131no—
184C2×#102—261no—
185C2×C4×C8C2×D1311yescharacteristic
186#390—261no—
187#388—262no—
188#384C2×D1311yescharacteristic
189#384C2×D1311yescharacteristic
190#380—261no—
191C4×C4⋊C4—131no—
192C4×C4⋊C4—261no—
193#340—261no—
194#340—261no—
195D4⋊C8—134no—
196C22×C13#38511yescharacteristic
197C22×C13#44911yescharacteristic
198C22×C13#44911yescharacteristic
199C22×C13#45011yescharacteristic
200C22×C13#45211yescharacteristic
201C22×C13#45311yescharacteristic
202C22×C13#45611yescharacteristic
203C2×D13—42no—
204C2×D13—42no—
205C2×D13—42no—
206C2×D13—81no—
207C2×D13—81no—
208C2×D13—81no—
209C2×D13—81no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—82no—
213C4×C13—161no—
214C4×C13#42711yescharacteristic
215C4×C13#42811yescharacteristic
216C4×C13C4×SD1611yescharacteristic
217C4×C13#44211yescharacteristic
218C4×C13#47611yescharacteristic
219C4×C13#47811yescharacteristic
220C4×C13#48211yescharacteristic
221C4×C13#48511yescharacteristic
222Dic13—42no—
223Dic13—42no—
224Dic13—81no—
225C22×D4—131no—
226C23×C4—261no—
227C22×C8—21no—
228C22×C8—261no—
229C22×C8—261no—
230C4×D4—132no—
231C4×D4—132no—
232C4×D4—261no—
233C4×D4—261no—
234#117—522no—
235#117—522no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—131no—
242C2×C4⋊C4—131no—
243C2×C4⋊C4—131no—
244C2×C4⋊C4C22⋊D1312yes—
245C2×C22⋊C4—261no—
246C2×C22⋊C4—262no—
247C2×C22⋊C4—262no—
248C2×C42—262no—
249C2×C42—261no—
250C2×C42C22×D1311yescharacteristic
251#107—522no—
252#106—44no—
253C4⋊C8—132no—
254C4⋊C8—261no—
255C4⋊C8—261no—
256C4⋊C8—261no—
257#102—522no—
258C4×C8—21no—
259C4×C8C4×D1312yes—
260#95—262no—
261#95—261no—
262C2×C13#162411yescharacteristic
263C2×C13#163111yescharacteristic
264C2×C13#165211yescharacteristic
265C2×C13#165411yescharacteristic
266C2×C13#185411yescharacteristic
267C2×C13#185911yescharacteristic
268C2×C13#186411yescharacteristic
269D13—82no—
270C24—261no—
271C2×D4—132no—
272C2×D4—261no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—261no—
276C2×D4—261no—
277C22×C4—22no—
278C22×C4—41no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—262no—
282C22×C4—262no—
283C22×C4—261no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4—521no—
287C22×C4—521no—
288C22×C4D4×D1311yescharacteristic
289C22×C4D4×D1311yescharacteristic
290C22×C4C2×C22⋊D1311yescharacteristic
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—262no—
295C2×C8—521no—
296C2×C8—521no—
297C2×C8—521no—
298C2×C8—521no—
299C2×C8—521no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—132no—
311C4⋊C4—132no—
312C4⋊C4—261no—
313C4⋊C4—261no—
314C4⋊C4—261no—
315C4⋊C4—261no—
316C22⋊C4—262no—
317C22⋊C4—262no—
318C22⋊C4—524no—
319C22⋊C4—1042no—
320C42—524no—
321C42—521no—
322C42—521no—
323C42C2×C4×D1311yescharacteristic
324C42#612711yescharacteristic
325C42Q8×D1311yescharacteristic
326C42#613111yescharacteristic
327C13#888911yescharacteristic, complemented, Sylow
328C23—262no—
329C23—521no—
330C23—521no—
331C23—521no—
332C23—521no—
333C23—521no—
334C23—521no—
335C23#8819111yescharacteristic
336D4—262no—
337D4—262no—
338D4—521no—
339D4—521no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—262no—
349C2×C4—262no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—522no—
355C2×C4—522no—
356C2×C4—522no—
357C2×C4—522no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4C4⋊C4×D1311yescharacteristic
362C2×C4#8814711yescharacteristic
363C2×C4#8814811yescharacteristic
364C2×C4#8815011yescharacteristic
365C2×C4SD16×D1311yescharacteristic
366C2×C4#8816811yescharacteristic
367C2×C4#8816811yescharacteristic
368C2×C4#8816811yescharacteristic
369C2×C4#8816911yescharacteristic
370C2×C4#8817011yescharacteristic
371C2×C4#8817011yescharacteristic
372C2×C4#8817011yescharacteristic
373C2×C4C4×C22⋊D1311yescharacteristic
374C2×C4#8820011yescharacteristic
375C8—24no—
376C8—522no—
377C8—1041no—
378C22—522no—
379C22—522no—
380C22—522no—
381C22—1041no—
382C22—1041no—
383C22—1041no—
384C22—1041no—
385C22#1171865011yescharacteristic
386C22#1171873811yescharacteristic
387C22#1171875611yescharacteristic
388C22#1171883011yescharacteristic
389C22#1171883311yescharacteristic
390C22#1171883311yescharacteristic
391C22#1171883411yescharacteristic
392C4—21no—
393C4—21no—
394C4—82no—
395C4—161no—
396C4—522no—
397C4—522no—
398C4—1041no—
399C4#1171851311yescharacteristic
400C4#1171852111yescharacteristic
401C4#1171852211yescharacteristic
402C4#1171852711yescharacteristic
403C4#1171852811yescharacteristic
404C4#1171853011yescharacteristic
405C4#1171853111yescharacteristic
406C4#1171853211yescharacteristic
407C2—1042no—
408C2#1311391711yescharacteristic
409C2#1311396011yescharacteristic
410C2#1311410311yescharacteristic
411C2#1311411711yescharacteristic
412C2#1311503411yescharacteristic
413C2#1311506111yescharacteristic
414C2#1311509411yescharacteristic
subgroupG/H
centerC23#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1844C2
socleC23×C13#120
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1844D13
hypocenterC13#8889
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13115592C2semidirect
5. #13112719C2semidirect
6. #13112676C2semidirect
7. C13×#1844C2semidirect
25. #11718051C4semidirect
123. #1844D13semidirect
327. C13#8889semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131177872
#131155922
#131148332
C2×#117180512
#131127192
#131126762
C13×#18442
#888913